On illuminating line segments in the plane

Let F be a family of n convex sets in the plane. A set of light sources S illuminates F if every point on the boundary of each element of F is visible from at least one element in S. We prove that if F is a family of n line segments, n ≥11, then ⌈2n/3⌉ light sources are always sufficient to illuminate F. If all the elements in F are parallel to the x or the y-axes, then F can be illuminated by at most ⌈(n+1)/2⌉ light sources.